A note on the K-epigraph

2021/06/30 by Armand Gissler, Gissler, Armand, Tim Hoheisel +1 · 1 citation
Computer Science · Mathematics · #Optimization and Variational Analysis #Advanced Optimization Algorithms Research #Fixed Point Theorems Analysis

paper · pdf · doi:10.48550/arxiv.2107.00117

Abstract

We study the question as to when the closed convex hull of a K-convex map equals its K-epigraph. In particular, we shed light onto the smallest cone K such that a given map has convex and closed K-epigraph, respectively. We apply our findings to several examples in matrix space as well as to convex composite functions.

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• Augmented Lagrangian methods for fully convex composite optimization

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